Remainder problem

(1) A number when divided by a divisor leaves a remainder of 24 . When twice the original number isdivided by the same divisor , the remainder is 11. What is the value of the divisor ?

(2) When 242 is divided by a certain divisor the remainder obtained is 8 . When 698 is divided by the same divisor the remainder obtained is 9 . However , when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 4 . What is the value of the divisor ?

Since the remainder is 24 and 11 respectively, we know that the divisor must be greater that 24 (otherwise a remainder of 24 is not possible) I used modular arithmetic to find the divisor to be 37, but simple guess and trial would have gotten you there!

By trial and error:

and...

By similar methods, the divisor must be greater than 4, 8 and 9... so start testing divisors from 10...